Homework Problems
7B-1 :
Entropy Change for a Heat Transfer Process
3 pts
Calculate the
entropy change of each reservoir when
1000 kJ of
heat is transferred directly from a hot reservoir at
1000 K to a cold reservoir at
400 K. Calculate the
entropy change of the universe for this process. Does this process violate the
principle of increasing entropy?
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7B-2 :
Rate of Entropy Increase for a Heat Transfer Process
3 pts
A hot reservoir at
944 K transfers
heat to a cold reservoir at
298 K. If the
rate of heat transfer is
25 kW, determine the
rate at which the
entropy of the two reservoirs
combined changes (in
kW/K) and determine if the
second law is satisfied.
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7B-3 :
Entropy Changes Associated with an Evaporator
4 pts
A refrigerator using
R-134a as the refrigerant
removes 200 kJ of
heat from its
refrigerated space. This heat is absorbed by a
mixture of
saturated liquid and
saturated vapor that enters the
evaporator at a pressure of
175 kPa. The
R-134a leaves the evaporator as a
saturated vapor. Determine
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7B-4 :
Power Output of an Isentropic Turbine
4 pts
An
isentropic turbine produces
shaft work as
R-134a at
275 psia and
225oF expands through the turbine and exits at
35oF. Assuming the turbine is
adiabatic, determine the
power output of the turbine
per lbm of
R-134a flowing through it.
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7B-5 :
Entropy Change for an Isobaric Heating Process
4 pts
A
piston-and-cylinder device holds
9.7 lbm of
water at
250 psia in a volume of
3.6 ft3.
Heat is added to the water until the temperature reaches
425oF. During this process, the
pressure in the cylinder remains
constant because the
piston moves freely. Determine the
change in the
entropy of the water in
Btu/oR.
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7B-6 :
Isentropic Compression of Water Vapor
3 pts
An
isentropic compressor takes in
H2O at
105 kPa and delivers it at
450 kPa. If the temperature of the feed is
180oC, determine the
temperature and
specific enthalpy of the
H2O at the compressor
outlet.
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7B-7 :
Isentropic Expansion of R-134a
4 pts
R-134a expands
reversibly and
adiabatically in a
piston-and-cylinder device from
80 psia and
120oF to
5 psia. If the cylinder contains
17.4 lbm of
R-134a, what are the
total work done
by the system during this process and the
final temperature of the
R-134a?
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7B-8 :
Vaporization of Water in a Rigid Tank
5 pts
An
electric resistance heater is used to heat the contents of an
insulated rigid tank that holds
23.1 kg of
H2O. Initially, the pressure in the tank is
150 kPa and
44% of the
mass inside the tank is
saturated liquid and the remaining
56% is
saturated vapor?. Power is applied to the heater until all of the H2O in the tank is saturated vapor. Determine the entropy change of the H2O and the total heat transfer during this process.
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7B-9 :
Expansion of Water into a Vacuum
5 pts
A
rigid tank is divided into
two equal parts by a wall. One part of the tank contains
0.74 kg of water at
100 kPa and
25oC. The other part is a
perfect vacuum. The wall is now
removed and the water expands to fill the
entire tank. A thermocouple indicates that the
final equilibrium temperature of the
H2O in the tank is
50oC. Determine the
entropy change of water and the
total heat transfer to the system during this process.
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7B-10 :
Isobaric Condensation of R-134a
5 pts
The refrigerant
R-134a is
cooled in a
piston-and-cylinder device from
190oF to
75oF. The piston
moves freely and the initial pressure is
200 psia. Determine the
specific entropy change of the refrigerant, the
work per lbm and
heat transfer per lbm during this process.
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7B-11 :
ΔS and Boundary Work for the Isobaric Expansion of Water
6 pts
Electrical work is done by an
electrical resistance heater on
H2O contained in an
insulated piston-and-cylinder device. The cylinder initially contains
2.4 L of
saturated liquid water at a pressure of
500 kPa. Assuming the
piston moves freely, determine the
total entropy change of the
H2O during a process in which
1875 kJ of
heat is transferred
into the water. What is the
boundary work for this process?
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7B-12 :
Reversible Expansion of R-134a in a Piston-and-Cylinder Device
4 pts
The refrigerant
R-134a expands
reversibly from
2 Mpa to
500 kPa in an
insulated piston-and-cylinder device. The cylinder
initially contains
15 L of
R-134a with a
quality of
1.0. Determine the
final temperature of the
R-134a in the cylinder and the
work done during this process.
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7B-13 :
Minimum Power Required for Adiabatic Compression of R-134a
4 pts
An
adiabatic compressor is used to increase the pressure from
105 kPa to
1.25 Mpa in a stream of
R-134a with a
volumetric flow rate of
1800 L/min. Determine the
minimum power that must be supplied to the compressor.
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7B-14 :
Reversible Compression of Steam in a Closed System
4 pts
Superheated steam is
reversibly compressed from
200 kPa to
1.4 Mpa in a
well-insulated piston-and-cylinder device. The cylinder
initially contains
0.175 m3 of steam at
250oC. Determine the
final temperature of the steam and the
work done
on the steam during this process.
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7B-15 :
Heat and Work in an Isothermal Expansion of Steam
5 pts
Saturated water vapor is contained in a
piston-and-cylinder device that is positioned in a
constant-temperature bath at
250oC. The
5.7 kg of steam inside the cylinder expands
reversibly and
isothermally to a final pressure of
1.2 MPa. Determine the
heat transferred between the
constant-temperature bath and the
water inside the cylinder as well as the
work done
by the
H2O inside the cylinder during this process.
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7B-16 :
Isentropic Compression of High Quality Steam
5 pts
Steam is compressed
isentropically to a final pressure of
5 MPa. The steam is initially at
25oC and has a quality of
91%. How much
work does this process
require, in
kJ/kg, if the process takes place in...
(a) A
closed system?
(b) An
open system?
(c) Explain why the answers to parts
(a) and
(b) are
not the same.
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7B-17 :
Isothermal Process In a Closed System
4 pts
The refrigerant
R-134a is contained in a
piston and cylinder device. The device is submerged in a circulating water bath that maintains the temperature of the
R-134a at
25oC. The
initial pressure inside the cylinder is
300 kPa. In the
final state, the
R-134a has a
quality of
0.35 kg vap/kg.Assuming the process is
internally reversible, determine the
total work per kg and the
heat transfer per kg that occurred during this process.
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7B-18 :
Interpreting Heat Transfer on a TS Diagram
3 pts
A working fluid undergoes the
reversible, two-step process shown in the
TS Diagram, below. Determine the
total heat transfer for the process,
Q13, in
kJ/kg.
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7B-19 :
Heat Transfer in the Two-Phase Envelope of a TS Diagram
3 pts
A working fluid undergoes the
reversible, two-step process shown in the
TS Diagram, below. During the process, the fluid evaporates and partially condenses. Determine the
total heat transfer for the process,
Q13, in
kJ/kg.
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7B-20 :
Interpreting Heat Transfer on a TS Diagram
3 pts
A working fluid undergoes the
reversible, two-step process shown in the
TS Diagram, below. Determine the
total heat transfer for the process,
Q13, in
kJ/kg.
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7B-21 :
Heat Transfer in the Two-Phase Envelope of a TS Diagram (AE)
4 pts
A working fluid undergoes the
reversible, two-step process shown in the
TS Diagram, below. Determine the
total heat transfer for the process,
Q13, in
Btu/lbm.
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7B-22 :
Entropy Change for Boiling Water
4 pts
Heat is transferred into
1 kg of
H2O contained in a piston and cylinder device with a free-floating piston that maintains the pressure at
500 kPa.
a.) Use
enthalpy values found in
thermodynamic data to calculate the
heat transfer required for a process in which the
H2O changes from a
saturated liquid to a
saturated vapor.
b.) Use the definition of entropy to determine the change in the
specific entropy of the
H2O in this process.
c.) Use
specific entropy values found in
thermodynamic data to calculate the change in the
specific entropy for the process. d.) Compare your answers for parts
(b) and
(c) and comment on the results.
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7B-23 :
Problem Title
4 pts
Calculate the
shaft work per kg produced as
steam expands from
4 MPa to
100 kPa in an
isentropic turbine. The inlet temperature is
500oC.
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7B-24 :
Problem Title
4 pts
The refrigerant
R-134a in a home refrigerator enters the compressor as a
saturated vapor at
-5oF. At the compressor outlet, the pressure is
250 psia. Determine the
minimum work required by this compressor in
Btu/lbm.
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7B-25 :
Entropy Change for a Pressure Cooker
6 pts
A
pressure cooker is a
rigid vessel with an
adjustable pressure relief valve. The pressure relief valve allows the user to set the maximum or
setpoint pressure inside the vessel. When the pressure exceeds the
setpoint pressure, the valve opens and some of the contents of the vessel, usually vapors, are allowed to flow out into the surroundings until the pressure in the vessel is reduced to the setpoint pressure. A
10 L pressure cooker with a setpoint pressure of
250 kPa contains
water at
250 kPa with a quality of
7 percent. During the cooking process,
heat is added from a
high-temperature thermal reservoir until the quality of the water inside the pressure cooker is
35 percent. Determine the
minimum entropy change (largest negative number) of the
high-temperature thermal reservoir during this process.
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7B-26 :
Stirred Pressure Cooker
6 pts
A
modified pressure cooker, similar to the one described in the
previous problem, allows
shaft work to be added to the contents of the pressure cooker by a
stirring impeller. Solve the previous problem for a stirred pressure cooker in which
65 kJ of
shaft work are added during the heating process. Determine the
minimum entropy change of the
thermal reservoir during this process.
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7B-27 :
Compression and Cooling of R-134a in a Closed System
4 pts
Five kilograms of
R-134a in a
piston and cylinder device at
-5oC and a quality of
95% undergo a two-step process. In
step 1-2, the R-134a is compressed
reversibly and
adiabatically to
1200 kPa. In
step 2-3, the R-134a is cooled
reversibly until all of the R-134a is a
saturated liquid.
a.) Sketch the two-step process on a
TS diagram. Be sure to include the
two-phase envelope and any relevant
isobars. Determine...
b.) the
work done on the R-134a in
kJ in
step 1-2,
c.) the
heat transferred from the R-134a in
kJ in
step 2-3.
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